We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to arbitrary sets of tensors of any depth, including matrices, can be interpreted as u…
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48 results for “tensor factor models”
Proposes FATTNN for tensor-on-tensor regression with improved prediction and reduced computation.
problem Tensor-on-tensor regression with complex tensor structures and nonlinear relationships.
method Integrates tensor factor models into deep neural networks to handle nonlinearity and reduce data dimensionality.
result Significant improvements in prediction accuracy and computational efficiency over traditional methods.
Tensor PCA for Factor Modelsecon.EM
Optimal tensor PCA for estimating factors and loadings in high-dimensional panel data.
problem Estimating factors and loadings in high-dimensional panel data with non-negligible correlations.
method Tensor Principal Component Analysis (TPCA) for estimating factors and loadings in a tensor factor model.
result Simple TPCA is optimal for strong factors and can be improved for weak factors with alternating least-squares iterations.
Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP te…
Proposes a new tensor factorization model for better link prediction in knowledge graphs.
problem Lack of information in treating missing and non-existing relations equally in tensor factorization models.
method Introduces a binary tensor factorization model with probit link to address the issue.
result Shows improved prediction accuracy and interpretability compared to existing models.
The paper tackles tensor factorization and completion from noisy data.
problem Sparse nonnegative tensor factorization and completion from partial and noisy observations.
method Minimizes the sum of maximum likelihood estimation and tensor norm with nonnegativity constraints.
result Error bounds and minimax lower bounds are established for the proposed model.
Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank dete…
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
SPIDER uses deep neural networks for streaming tensor factorization.
problem Lack of effective approach for deep tensor factorization of streaming data.
method Bayesian neural networks with spike-and-slab prior, Taylor expansions, moment matching, and EPI framework.
result Effective incremental updates for latent factors and NN weights.
TATD predicts missing entries in time-evolving tensors by exploiting temporal dependency and sparsity.
problem Predict missing entries in time-evolving tensors with temporal dependency and sparsity issues.
method TATD (Time-Aware Tensor Decomposition) integrates temporal dependency and time-varying sparsity through a smoothing regularization with Gaussian kernel and alternating optimization.
result TATD achieves state-of-the-art accuracy for decomposing temporal tensors.
Causal Deep Learningcs.LG
Causal deep learning tackles causal inference using tensor factor analysis.
problem Addressing causal questions in data using neural networks.
method Tensor factor analysis and neural network architectures (causal capsules, tensor transformer, multilinear projection algorithm).
result Derives deep neural networks for causal inference with tensor factor analysis.
NNEinFact fits any nonnegative tensor factorization quickly and accurately.
problem Limited user-friendly tools for fitting tailored nonnegative tensor factorizations.
method NNEinFact is an einsum-based multiplicative update algorithm that fits any nonnegative tensor factorization.
result NNEinFact converges to a stationary point of the loss, supports missing data, and fits tensors with hundreds of millions of entries in seconds.
Gradient descent in tensor factorization favors low-rank solutions.
problem Tackling implicit regularization in tensor factorization problems.
method Gradient descent with small random initialization for overparametrized tensor factorization.
result Gradient descent leads to implicit regularization towards low tubal rank solutions.
Robust Bayesian Tensor Factorization with Zero-Inflated Poisson Model and Consensus Aggregationstat.ML
Paper introduces ZIPTF and C-ZIPTF for better tensor factorization of zero-inflated count data.
problem Inefficient tensor factorization for zero-inflated count data, especially in scRNA-seq.
method Zero Inflated Poisson Tensor Factorization (ZIPTF) and Consensus Zero Inflated Poisson Tensor Factorization (C-ZIPTF).
result ZIPTF and C-ZIPTF improve tensor factorization accuracy and consistency for zero-inflated count data.
A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient t…
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country took action toward country at time "---known as dyadic events---in order to form an…
Enhances knowledge graph completion with mixed geometry tensor factorization.
problem Capturing nuanced distributional properties in knowledge graphs.
method Combines Euclidean and hyperbolic geometries for tensor factorization.
result Improves link prediction accuracy with fewer parameters.
CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem e…
Deep tensor factorization benefits from implicit regularization with polynomial growth.
problem Tensor factorization's implicit regularization effect in deep networks is not well understood.
method Investigated the implicit regularization in deep tensor factorization, showing polynomial growth.
result Implicit regularization in deep tensor factorization grows polynomially with depth, improving estimation accuracy and convergence.
GLSKF improves tensor completion by capturing both global and local variations.
problem Tensor completion with missing entries, especially in data with spatial or temporal side information.
method Integrates smoothness-constrained low-rank factorization with a locally correlated residual process.
result GLSKF achieves superior performance and scalability on real-world datasets.
We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed counts as well as infer the rank of the decomposition. Moreover, leveraging a repa…
Proposes a nonparametric tensor factorization for sparse data.
problem Handling sparse tensor data with structural and interpretability benefits.
method Hierarchical Gamma processes and Poisson random measures for tensor-valued process, Dirichlet processes for sampling entry indices, Gaussian processes for values.
result Demonstrates superior performance on benchmark datasets.
Implicit Regularization in Hierarchical Tensor Factorization and Deep Convolutional Neural Networkscs.LG
The paper explains implicit regularization in hierarchical tensor factorization and deep CNNs.
problem Understanding implicit regularization in complex neural network architectures.
method Theoretical analysis using dynamical systems to overcome challenges in hierarchy.
result Established implicit regularization towards low hierarchical tensor rank, equivalent to locality in CNNs.
Efficiently factorize tensors in streaming data with coreset selection.
problem Efficiently factorize tensors in streaming data.
method Online filtering and kernelization techniques to select a coreset of vectors.
result CP decomposition of coreset approximates full data tensor decomposition.
Probabilistic Temporal Tensor Factorization (PTTF) is an effective algorithm to model the temporal tensor data. It leverages a time constraint to capture the evolving properties of tensor data. Nowadays the exploding dataset demands a large scale PTTF analysis, and a parallel solution is critical to accommodate the tre…
We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To capture such complex structures, a double core tensor (DCOT) factorization mode…
Paper proposes C-STM for multimodal neuroimaging data classification.
problem Multimodal neuroimaging data fusion for better classification.
method Coupled Support Tensor Machine (C-STM) using latent factors from ACMTF.
result C-STM achieves better classification performance than single-mode classifiers.
A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model …
Automates supervised learning pipeline design with matrix and tensor factorization.
problem Designing effective supervised learning pipelines with many choices.
method Uses matrix and tensor factorization to model pipeline search space and develops greedy experiment design protocols.
result Demonstrates the effectiveness of the approach on real-world classification problems.
Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single…
Graphical model for factorization and completion of relatively high rank tensors by sparse samplingstat.ML
Sparse sampling method for tensor factorization and completion of high rank tensors.
problem Completion of high rank tensors with missing data in recommendation systems.
method Sparse measurements and message-passing algorithms in a high-dimensional limit.
result Theoretical insights and performance analysis of tensor factorization in dense limit.
Proposes a method for tensor completion with sparse factors and missing data.
problem Recovering nonnegative data from noisy observations with missing values.
method Sparse nonnegative Tucker decomposition with norm for sparsity, maximum likelihood estimation, and error bounds.
result The method outperforms existing tensor-based or matrix-based methods in nonnegative tensor data completion.
Bayesian Poisson-Randomized Gamma Tensor Factorization with Application to International Trade Flowsstat.ME
Bayesian hierarchical tensor factorization model for international trade flows
problem Sparse semi-continuous tensor data modeling
method Bayesian hierarchical tensor factorization with Poisson and Gamma models
result Identifies multiway dependence in trade flows
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspond…
We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood, using a zero-truncated Poisson likelihood for binary data allows our model to scale …
Efficiently factorizes coupled matrix tensor data for better accuracy and speed.
problem Poor computation efficiency in existing N-CMTF algorithms.
method Column-wise element selection to prevent frequent gradient updates.
result More accurate and computationally efficient factorization.
Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.
problem Jointly analyze matrices and tensors with irregular/ragged data.
method Alternating Optimization (AO) and ADMM for fitting PARAFAC2-based CMTF models with various constraints.
result Accurately recovers underlying patterns using various constraints and linear couplings.
New method improves sales forecasting accuracy using tensor factorization.
problem Improving sales forecasting accuracy in retail businesses.
method Advanced Temporal Latent-factor Approach to Sales forecasting (ATLAS) using tensor factorization.
result Accurate and individualized prediction for sales across multiple stores and products.
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order word co-occurrence based arrays, or \textit{tensors}. We present four word embedd…
New algorithm for online tensor factorization with provable guarantees.
problem Factorizing structured tensors with unknown factors and non-convex optimization.
method Online CP/PARAFAC decomposition via dictionary learning with incoherence and sparsity constraints.
result Exact recovery of tensor factors at a linear rate under mild conditions.
Orthogonalized ALS: A Theoretically Principled Tensor Decomposition Algorithm for Practical Usecs.LG
The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a modification of the ALS approach that is as efficient as standard ALS, but provably rec…
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …
Unified model for tensor completion using low-rank and sparse Tucker decomposition.
problem Estimating missing data from incomplete tensor measurements.
method Unified low-rank and sparse enhanced Tucker decomposition model with ADMM.
result Our model achieves higher recovery accuracy on various real-world data sets.
Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regressionstat.ML
BKTR models spatiotemporal data with scalable tensor regression.
problem High computational cost in applying STVC to large-scale spatiotemporal data.
method Summarize STVC coefficients in a tensor, reformulate as low-rank tensor regression, incorporate GP priors for local dependencies.
result BKTR efficiently models large spatiotemporal datasets with reduced parameters and local dependencies.
The paper analyzes implicit regularization in tensor factorization using neural networks.
problem Understanding implicit regularization in tensor factorization.
method Dynamical systems perspective and gradient descent analysis.
result Gradient descent induces a form of greedy low tensor rank search.
Proposes a new tensor decomposition method for functional temporal data with adaptive complexity.
problem Challenges in temporal tensor decomposition for general tensor data with continuous indexes.
method Encodes continuous spatial indexes as learnable Fourier features and uses neural ODEs for temporal trajectories. Introduces a sparsity-inducing prior for complexity adaptation.
result Significantly outperforms existing methods in prediction performance and robustness against noise.
We propose an algorithm for the non-negative factorization of an occurrence tensor built from heterogeneous networks. We use l0 norm to model sparse errors over discrete values (occurrences), and use decomposed factors to model the embedded groups of nodes. An efficient splitting method is developed to optimize the non…
Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. …